A class of local gauge theories based on compact semisimple Lie groups is studied in the limit of infinite gauge coupling constant (g = infinity). In general, in this limit, the gauge fields become auxiliary in all gauge theories, and the system develops a richer structure of constraints. Unfortunately for most gauge theories, this limit turns out to be too singular to quantize and the theory ceases to be renormalizable. For a special class of gauge theories, however, where there are no fermions and there is only one multiplet of scalars in the adjoint representation, we prove that a consistentmore » renormalizable quantum theory exists even in this very singular limit. We trace this exceptional behavior to a new local translationlike symmetry in the functional space that this class of gauge models possesses in the limit of infinite gauge coupling constant. By carrying out the constraint analysis, evaluating the Faddeev-Popov-Senjanovic determinant, and doing the functional integrations over the canonical momenta, the gauge fields, and most of the components of the scalar fields, we obtain an extremely simple result with no non-Abelian structure left in it. For example, for the group SU(2), the final answer reduces to the theory of a one-component self-interacting real phi/sup 4/ scalar field theory. Throughout this paper, we use functional methods and make no approximations; our results are nonperturbative and exact. We also discuss some of the possible implications of our results.« less

The Cucchieri-Mendes bounds for the gluon propagator are discussed for the four dimensional pure-gauge SU(3) theory. Assuming a pure power law dependence on the inverse of the lattice volume, the lattice data gives a vanishing zero-momentum gluon propagator in the infinite-volume limit in agreement with the Gribov-Zwanziger horizon condition but contradicting the SU(2) analysis. The results are robust against variations of the lattice volumes and corrections to the power law. Our analysis considers also more general ansatze that, although not conclusive, open the possibility of having D(0){ne}0 in the infinite-volume limit. A solution to this puzzle requires further investigations.

The role of sin/sup 2/THETA/sub W/ in the Weinberg--Salam SU(2) x U(1) model is reviewed. Effects of radiative corrections on neutral current determinations of this parameter are described. It is pointed out that such effects can potentially shift the real value of sin/sup 2/THETA/sub W/ away from the present experimental world average of 0.23 +- 0.015. Predictions by grand unified gauge theories for the effective low energy value of sin/sup 2/THETA/sub W/ are also reviewed. Implications of those results for the Georgi--Glashow SU(5) model and the lifetime of the proton are outlined. Combining that analysis with the Goldman--Ross estimate formore » the super-heavy boson mass M/sub S/approx. =3 x 10/sup 14/ GeV., the SU(5) model is found to predict sin/sup 2/THETA/sub W/approx. =.21--.22 and a proton lifetime tau/sub p/approx. =10/sup 29/--10/sup 30/ yrs.« less